114} ESSAY ON PROBABILITIES. 



never enable us to tell what face of a die will be turned 

 up in any one instance, nor would the maxims of our 

 science be worth putting into practice with respect to 

 an event which is to happen only a few times. If a 

 man were determined to run six hazards, and never to 

 gamble afterwards, say if he were determined to wager 

 twice upon a pair of dice giving doublets, I should 

 think it perfectly immaterial whether he accepted an 

 even wager, namely 5 to 1, or not. For though, in the 

 long run, only one throw out of six will give doublets, 

 yet the probability that six throws will give such a pair 

 once at least is not very great. It is as a provider of 

 general rules of conduct that the science is valuable ; 

 the adherence to rules being desirable on precisely the 

 same principles as those which obtain in morals or legis- 

 lation, no maxim of which will be found to meet every 

 case which will occur. 



It is an assumption of this theory that nothing ever 

 did happen, or ever will happen, without some particular 

 reason why it should have been precisely what it was, 

 and not any thing else. Conceive it possible that a ball 

 which is white might have been black, without the 

 alteration of any action or circumstance which took 

 place in time previous to the moment at which the 

 ball is shown, and the foundations of the theory of 

 probabilities have ceased to exist in the mind which has 

 formed that conception. There is no one but will admit, 

 that out of a box, which contains nothing but two black 

 balls, nothing but black balls can be drawn ; and that 

 out of a box which contains only two white balls, 

 no black balls can be drawn. The difficulty lies in a 

 clear perception of the remaining assertion ; namely, 

 that when the box contains one white ball and one black 

 ball, a very large number of drawings will give as 

 many white as black nearly, and the more nearly the 

 greater the number. This proposition might be proved 

 in three ways : firstly, by actual experiment ; secondly, 

 by showing that out of all the possible cases which can 

 happen, those in which black and white are equal, or 



